The Generalization as a Tool to Develop the Algebraic Thinking Process
Abstract
In this paper, we propose a reflection on how pupils use algebraic generalization and symbolization during the transition from a geometric thinking process to the algebraic one. This paper describes a new method/idea based on the use of geometric patterns in some proposed learning situations with the primary aim of understanding how this use may enable learners to develop and improve their algebraic thinking process. Thus, we proposed to a sample of pupils from 10 to12 years old to draw some geometric figures of squares and rectangles and asked them to conjecture the three well-known remarkable identities, (a+b)2, (a-b)2 and a2-b2. The students are supposed to put these squares and rectangles together to form a single square or a rectangle and to deduce these identities. Our analysis focuses on videos capturing student behavior using patterns to develop some generalization of the algebraic process on data collected during student interviews and on the difficulties of students deriving algebraic formulas from some geometric patterns.
Keywords: generalization, algebraic thinking process, geometric thinking process, patterns in education.
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